How do I set third person controls in bge?
Change your motion actuators to global instead of local


Try clicking on the L on the right. also does your character rotate mid game or just move left, right, forwards, and backwards?
If you set the motion to global, the movement would be always in the same direction even if your character rotates. So as long as your camera doesn't rotate, the movement should be always the same and therefore the same with respect to the camera.

Hope this helps :)